Question: Simplify the following expression: $ a = \dfrac{-6t}{t - 10} - \dfrac{-7}{3} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-6t}{t - 10} \times \dfrac{3}{3} = \dfrac{-18t}{3t - 30} $ Multiply the second expression by $\dfrac{t - 10}{t - 10}$ $ \dfrac{-7}{3} \times \dfrac{t - 10}{t - 10} = \dfrac{-7t + 70}{3t - 30} $ Therefore $ a = \dfrac{-18t}{3t - 30} - \dfrac{-7t + 70}{3t - 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-18t - (-7t + 70) }{3t - 30} $ Distribute the negative sign: $a = \dfrac{-18t + 7t - 70}{3t - 30}$ $a = \dfrac{-11t - 70}{3t - 30}$